International Conference

The many dimensionsof poverty

Brasilia, Brazil – 29-31 August 2005Carlton Hotel

Conference paper

The

many dimensions of poverty

E M B A R G OThis text is on embargo until 29 August

Think Global, Act Local: Social CreditBased on the MDGs

Marcelo Cortez NeriGetúlio Vargas Foundation (FGV) and Brazilian Institute of Economics

Marcelo Casal XerezGetúlio Vargas Foundation (FGV) and Brazilian Ministry of Finance,Rio de Janeiro, Brazil

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Think Global, Act Local:

Social Credit based on MDGs Marcelo Côrtes Neri ( mcneri@fgv.br )

Center for Social Policies at FGV and EPGE/FGV

Marcelo Casal Xerez

EPGE/FGV and Brazilian Ministry of Finance

Abstract: This project discusses the economic rationality and practical problems related to a

system of social targets and credit based on the Millennium Development Goals (MDGs), as a

way for the federal government to increase efficiency in the use of its social budget transferred to

local governments (states, municipalities etc).

The Millennium declaration mediates social indicators and deadlines to be pursued at the global

level. As the fight against poverty transcends mandates and boundaries, the first proposal stud ied

is that specific locations—in particular, those at the sub-national level—announce a commitment

with the global targets specified. In practice, this would involve that states and municipalities,

other than nations, challenge their respective population to reach the proposed targets. Since the

deadline for the global goals outlasts the time frame of a single government, it inhibits

discontinuity of actions between political mandates. In other words, international MDGs enjoy

the attribute of being exogenously given, which allows not only time consistency in decisions,

but a better integration of social efforts across different government levels. The second proposal

studied is that the distribution of resources transferred from higher to lower government levels be

linked to social performance trough a social credit contract. We discuss whether it is the case,

why and what would be the desirable characteristics of such contracts.

The objectives of this paper are divided in two parts: First, we offer a theoretical framework that

allows the designing of different contract clauses in different environments (e.g. static and

dynamic; with and without imperfect information, with and without complete contracts; and

different commitment technologies). This analysis is performed by developing extensions of a

standard principal-agent model. The results show that the use of the focalization criteria where

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the poorest municipalities get more resources may lead to adverse incentives to poverty

eradication. We also show tha t unconditional transfers from the federal government crowd-out

local social expenditures. We argue in favor of the use of contracts where the greater the

improvement in relevant social indicators, the more resources each municipality would receive.

The introduction of imperfect information basically generates a penalty to the poor segments in

areas where local governments are less averse to poverty. Another advantage of this type of a

social credit contract is to reduce the problem of political favoritism when certain social groups

receive greater attention from specific governments. With the establishment of social targets it

becomes possible to generate proper incentives so that social spending is distributed more

equitably between groups. Second, we analyze how specific communities can adhere directly to

the Millennium Development Goals (MDGs) as way to coordinate social efforts worldwide with

local budgetary implications.

Key words:

1. Social targets

2. Poverty

3. Inequality

4. Social spending

5. Social welfare

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1- General Motivation:

The management of Brazilian social policy has become more complex and challenging

than ever. The decentralization of public actions allied to the growing involvement of NGOs and

private firms creates a widespread diversity of simultaneous actions. On the other hand, the

internationalization process of economies, concomitant with contagious macroeconomic

instabilities, broadens the scope of opportunities to the realization of transfers of resources and

social technology between countries.

The question interesting us is: how should we increase the returns obtained by society

from this myriad of actions? It is up to the diverse levels of public activity (multilateral entities,

several levels of the state, and civil society) to act simultaneously towards the same goals. These

involve the coordination of diffused efforts through the settlement of targets and the design of

mechanisms providing the incentives to achieve them.

The Millennium declaration, recently promulgated, mediates not only social indicators, as

well as values and deadlines to be pursued at the global level. Our proposal is that specific

locations—in particular, those at the sub-national level—announce a commitment to the global

targets as they have been specified. In practice, this would involve that states and municipalities,

other than nations, challenge their respective populace to reach the proposed auspicious targets.

An example: state A, or district B, would adhere to the target of reducing by one ha lf the

proportion of its population with income per capita below US$1.00 daily at PPP, by the year

2015. The recent Brazilian experience with inflationary targets enlightens the strength of tangible

objectives.

Now why should we only adhere to the Millennium goals and not others? a) The

proposed indicators have already been formulated, monitored and benefit from inherent

credibility. b) The uniformity of the goals may contribute to the convergence of social efforts at

the global scale, by guaranteeing a positive externality. c) The fact that the deadline for the

global goals outlasts the mandate of a single government inhibits discontinuity of actions

between political mandates; external goals tend to establish temporal consistency in decisions. d)

The perceived exogeneity of the goals across localities also provide a neutral ground for

agreements across different government levels, allowing a better integration of social efforts. The

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goals ideally belong to society and its citizens, as being perceived as independent from the

idiosyncrasies of specific governments.

Aside from the coordinating and mobilizing characteristics of the social targets, the

conditioning of the financial aspect to the observed social outcome—be that considering

individuals or levels of government—is an interesting principal. The same spirit of cash for

education programs of rewarding poor families whose children attend school such as Bolsa-

Escola in Brazil or Progressa in Mexico can be applied to the annual reallocation of the social

budget at numerous administrative levels. The process of rewarding, with additional resources,

those units progressing swiftly, may be applied towards the lower levels of government: from the

federal to the state realm, from the state to their respective municipalities and from the latter to

their respective administrative regions. The Demographic Census form the Brazilian Statistical

Bureau (IBGE) provides recent information constituting the stepping-stone for these various

geographical levels.

Following this line of reasoning, the magnitude of the external debt forgiven for heavily

indebted poor countries (HIPC), currently in place, should also consider the future path of these

nations’ social indices. Those attaining financing from lost funds tend to lose their motivation.

On many occasions, the best remedy against poverty is not charity, but credit instead. There is no

doubt that the core of social action should be upon the poorest, but nonetheless, those moving

towards the emancipation of their wanting should be rewarded. The main comparative advantage

of being poor is the relative capacity of prospering. Future success should also be rewarded,

instead of only compensating for past failures.

The social credit mechanisms discussed here can also be perceived as a process of

converting social debt into financial wealth. Think it as a measure the social debt the amount of

resources lacking in a given society for a given period of time to come, say T years1. This

society would be entitled a given cash flow as social indicators show that it is emancipating from

its social debt. One may think that efficiency is not a comparative advantage of a poor society.

However, one of the few advantages of being poor is the ability to improve. For example, if 50%

of the children are out of school, one may double the initial figure, while if the starting point is

1 Perhaps the easiest example visualize is the present value of the average income gap (P1) times the population size discounted over T periods.

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97% of the children in school, there is not much room for improvement. In this way in the case

of social credit equity and efficiency walk hand in hand.

The social target’s main problem is related particularly to the short run, given the

presence of shocks. The result obtained by the social protagonist depends on factors beyond his

reach, as the outcome does not depend solely on his efforts or skill. Thus the importance of using

a relative evaluation schemes is made clear. The selection of a system capable of international

comparisons allows us to place each country within the international norm. The system of

incentives should be announced a priori and the relative performance should be evaluated a

posteriori. Everything functions as a system of credit in which the financial debt from social

projects can be reduced in view of social advancements. The advantage of the social credit

apparatus is, if well designed, to attract better social actors and induce them to undertake the best

practices.

Many social programs are based upon the transfer of federal government’s funds to the

poorer regions. Obviously, the expenditure of money in these regions results in an improvement

for the local population’s living conditions. However, what is not being evaluated—and what

establishes the core of this work—is to know whether the final result reached could have been

better.

It is impossible for the federal government to know which are the specific needs of each

locality within the country. In a region where the HDI2 struck as low, it would rarely have more

information than the local government about who are the poor and what is the best way to help

them, for the mayor is the one who better understands the region’s intricacies. For this reason, it

is only natural for the local government to be responsible for determining what must be done.

The federal government should have the assignment of establishing a partnership with

municipalities, via target contracts, and monitor how funds are being spent and which are the

goals being achieved.

Facing this situation, we analyze the mechanisms for social targets in relation to the

fulfillment of targets by the ones receiving the funds, as pre-established in contract. The

mechanisms being analyzed are based upon the selection of an optimum level of governmental

transfers—for example, from the federal government to municipalities.

2 The HDI is an index composed of health, education and income indicators, being that each one of these three components has the same weight in the index.

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In the studied system of social targets, it is the government’s responsibility to establish a

group of possible contracts to be asserted between the federal government and the municipality.

Such contracts contain clauses to establish the targets to be reached and the value to be

forwarded from the federal government to the local one for the accomplishment of these goals.

The subjacent idea is that, if the municipality does not reach the established targets, it will not

receive the funds, or receive only an amount proportional to the accomplishment reached. This

way, what is established between the federal and local governments is similar to a hiring

contract, in which the federal government hires the municipality so that it may run a service in

the social area. However, in a more realistic situation, so that the targets may be reached, first the

municipality must receive the funds, and only after the targets are checked. We can consider the

funds received by the local government as an advanced payment – called here as Social Credit -

so that the municipality may carry out a specific service pre-determined in the contract—which

establishes the goals to be accomplished. In case the targets are not reached, the municipality

starts to have a debt with the federal government for the non-fulfillment of an agreed service.

The debt is the difference between the advanced payment and payment estimated by the contract

for the complete results to be accomplished.

The main issue in this type of model is the establishment of the targets to be reached and

the manner of paying for the obtained result. The paper develops extensions of a standard

principal-agent framework to discuss the relationship between the federal government and local

governments. It is organized as follows: section two presents the basic framework of analysis.

The first part of section three extends static models with perfect information in various

directions, namely: 1) autharchy; 2) unconditional transfers from the federal government to

municipality; 3) perverse incentives where the poorest municipalities get more resources; 4)

social targets where the greater the improvement in relevant social indicators, the more resources

each municipality would receive. 5) political favoritism when certain groups of poor receive

greater, or smaller, attention from specific governments. 6) political favoritism with social

targets. The fact that youth is underrepresented in the electoral market (i.e., individuals below 16

years of age are not allowed to vote) makes social expenses on children less palatable to

politicians, opening room for the adoption of social targets to make expenditures more equitable.

The final part of section three analyses the implications of the introduction of imperfect

information in the static model with two types and a continuum of types of agents.

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Section four develops dynamic models with different renegotiation possibilities, namely:

1) Full Commitment when there is not the possibility of any type of renegotiation of contracts

across periods, even if all parties involved agree about a change. 2) Long term commitment

when renegotiation is allowed if both parties are in agreement. 3) No commitment when the

government does not have the commitment to maintain the contract established in the first

period. 4) Incomplete contracts. Finally, section five presents the ma in findings of the paper.

2 – Basic Model

The model is based on the structure of principal and agent. In our case, the federal

government (F) may be regarded as the principal. The agents are the municipal governments

(M), here forth referred to as municipalities. Aside from the federal and municipal governments,

we have the poor (P), whom the social targets to be established in contract between the

government and the municipality will be affecting.

A basic hypothesis of the model is that the federal and local governments seek to improve

living conditions of the poor, for this means to the representatives an increase in their chances of

reelection. In the model, their level of income will measure this improvement in living conditions

of the poor. This is equivalent to saying that the social target sought is the increase of average

income of the poor.3

However, the key issue when discussing poverty reduction, is to know who will pay the

bill. If on one hand, the reduction of poverty brings electoral benefits, on the other hand, for it to

occur, it is necessary to invest in income transfer programs, which reduces the available budget

for other types of investments.

The local government would love it if the federal government made large social

investments in its region, and preferably, if such expenses did not include a counter-measure

from the municipality. It would be the authentic “free lunch.” The federal government would

spend part of its budget, and the municipality would obtain political gains. The same analysis is

valid in the opposite sense.

3 However, an identical analysis can be made with other social indicators or even with an average of them, such as occurs with Human Development Index—HDI—or with the Life Conditions Index—LCI (Índice de Condições de Vida—ICV). Where one reads income, child mortality, school attendance rate, HDI, etc. could be placed instead. The choice of the target income throughout the text has the objective of trying to make the model more intuitive.

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Such as Besley (1997), Gelbach and Pritchett (1997), and Azam and Laffont (2001), we

assume that the federal government, as well as the local one, has an aversion to poverty, which

may be modeled through a utility function, in which the poor’s income is seen as a positive

externality for the federal government as well as for the local government. For a matter of

simplicity, we assume that the government’s and the municipality’ utility functions are quasi-

linear, in the available budget, and strictly concave in the poor’s income. This way, the

government and the municipality are concerned with absolute poverty, instead of relative

poverty. The desire to help the poor does not depend, however, on the total budget, but only on

the poor’s income level.

The utility functions for the federal government , UF, and for the municipality, UM, are

respectively given by:

UF = GF + NP. v(YP)

UM = GM + NP.θ.v(YP)

Being that v(0) = 0, v´(YP) > 0, v´´(YP) < 0, limYp→0 v´(YP) = +∞ e limYp→+∞ v´(YP) = 0

Where,

GF: is the budget available to the federal government. It is considered that the government has a

total budget (own) of YF. Part of this budget may be transferred, T, to income programs directed

towards the poor. The difference YF – T = GF. This is the budget the government has for all other

necessary expenses. Obviously, the greater the available budget, the larger will be the

government’s utility.

GM: budget available to the municipality. Such as the government, the municipality also has its

own budget, YM. The available budget, GM, is what is left after the transfer performed by the

municipality to the poor.

θ: is the parameter expressing the aversion to poverty of a local government. Different mayors

may present different degrees of aversion to poverty. The absence of the parameter θ in the

government’s utility function expresses the normalization that it has a parameter of θ = 1.

NP: number of poors in a municipality.

We will assume that the local government is the one better aware of the local reality, and

therefore more capable than the federal government of identifying who really are the poor within

the region. The local government also has better conditions for managing and implementing an

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income transfer program to its locality. This way, all government transfers will be directly made

to the municipality, which will be responsible for transferring it to the poor.

In relation to the poor’s utility, UP, the only consideration undertaken by us will be that if

grows in accordance to income: P PU ´(Y ) 0≥ . The greater the income, the poor will be better off.

From here on we will sometimes refer to the federal government as the principal and to

the local government as the agent.

3 – Static Model

In this chapter, we divide the analysis in two parts. One refers to the case of complete

information, when the principal knows the type θ of the agent. In the other case, there is an

information asymmetry, derived from the non-observance type of agent. This asymmetry allows

for some agents to attain informational income, which can be seen as a counterpart that the agent

charges to reveal its true type.

3.1 – Complete Information

In this case, the government knows the mayor’s (municipality’s) aversion to poverty. It is

an ideal situation, as it is difficult to know this type of information. However, the study in this

case is important for some reasons. One of them, is that it allows us to compare the differences in

the results of social policies when the government does not know the type of municipality.

Besides this, we can obtain some interesting intuitions, which are the key factors in determining

the result of social policies.

3.1.1 – Autarchy (A)

The basic situation is that in which the government does not carry out any transfer to the

municipality. In this case, the municipality’s incentive to transfer income to the poor is

exclusively due to the positive externality that an improvement in the poor’s living conditions

results to the local government. In this situation, the municipality solves the following problem:

Max GM + NP .θ . v(YP)

YP

s.t: GM + NP . YP ≤ YM

The first order condition (FOC) of the above problem is:

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1 2

AP

1 2 P P

1v´(Y ) logo

Y Y

=θ

θ > θ ⇒ >

However, the poor’s income in autarchy, APY , is determined by the coefficient of the local

government’s aversion to poverty. The larger this coefficient, the larger will be the poor’s

income. Governments more concerned with the poor’s social situation implement better income

transfer policies. It is observed that the poor’s income does not depend upon the number of poors

nor on the municipality’s budget. This is a result of the quasi- linear utility function chosen for

the local government.

For the municipality of type θ, the utility after the transfer is :

A A AM M P P P PU( ) U Y N .Y N . .v(Y )θ = = − + θ

Further ahead, when we deal with the federal- local relation, this equation will be the

minimum utility that the municipality will take into consideration to accept the establishment of

a contract estimating social targets as a countermeasure to the governmental transfers.

3.1.2 – Unconditional Transfer (TI)

Suppose the federal government chooses to invest in determined places, transferring

funds for the municipality to invest in a social area. As we have previously calculated, in our

model we will always suppose that the government transfers funds to the municipality and the

local government is the one in charge of implementing the social policies. In this case, let’s

suppose the government does not establish any condition (i.e., social target) in what refers to the

accomplishment of results by the municipality. It only transfers unconditionally a fixed fund of

TI. For the municipality, the problem to be solved is:

M P P

PI

M P P M

Max G N . .v(Y )Ys.a: G N .Y Y T

+ θ

+ ≤ +

Solving the problem, the first order condition obtained is:

I I AP P P

1v´(Y ) Y Y= ⇒ =

θ

That is, the poor’s income in autarchy or in a situation in which an unconditional transfer

occurs is the same.

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Proposition 1: If the federal government performs unconditional transfers to the local

governments, the poor’s situation does not change.

Besides this, I AP PY Y

I I I I I A AM M P P P P M P P P P

I A I I AM M M M

U Y T N .Y N . .v(Y ) Y T N .Y N . .v(Y )

U U T U U

=

= + − + θ = + − + θ

= + ⇒ >

and I A I I AF F F FU U T U U= − ⇒ >

Defining the funds destined, by the municipality, to the social program as being TM, we have

that: I I A AM P P P P MT N .Y N .Y T= = =

What is observed in this type of transfer is that the local government does not use the

funds transferred to improve the poor’s situation, but starts to include it in its available budget.

Another interpretation is to consider that the local government really destines the funds received

to the social programs. However, in the same quantity as that received, it stops directing part of

its own budget to the social area, accounting for these funds as available budget. It would be a

type of crowding-out effect, where the government’s investment reduces (misplaces) the

municipality’s own investments.

In this way, the local government’s utility increases, for the poor will be as well off as

they would in autarchy, but the available budget increases. The government, on the other hand,

will be worse off, for the poor will not have improved, and the available budget will be smaller.

3.1.3 – Perverse Incentive (PI)

Suppose the government decides to help more the municipalities where the poor are

poorer, so that the smaller the poor’s income, the greater is the income per capita transfer carried

out by the government to the municipality. For this, we suppose the government transfers the

difference between YP, and a basic estimated value, K. Soon, the total transfer that a municipality

is entitled to is:

PP NYKT ).( −=

The municipality, knowing that it will be entitled to this transfer, solves the problem of

determining how much it will invest in the social area, that is, what is the income NP.YP that it

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will transfer to the poor. The better the poor’s situation, the less the municipality will received

from the government, but on the other hand, the greater is the externality created by the poor’s

situation. The municipality’s problem can be described as:

Max GM + NP .θ . v(YP)

YP

s.t: GM + NP . YP ≤ YM + (K – YP).NP

Solving for this, we have:

θ2

)´( =IAPYv such that,

AP

IAP YY <

The consequence of establishing a system in which the greater the poverty, the greater the

federal government’s investment in the region, without any counter-measure regarding the

results, is the creation of perverse incentives. This is due to the fact that it stimulates the

municipal government to reduce its social investments, so that it can receive more transfers. The

final investment ends up being smaller than in the case of autarchy.

3.1.4 – Transfer Conditional on the Fulfillment of Social Targets (Tc)

Until now we have studied cases in which the government either undertook no transfers

of any kind to social programs, or it did so without establishing any type of social target that

could serve as a condition for the municipality to receive funds. Let’s now study how the

establishment of social targets can increase efficiency in the use of public money.

Let’s suppose that the principal offers a contract to the agent under which a transfer

conditioned upon the achievement of a pre-determined income social target, Yp is estimated.

The principal’s problem is defining a contract. (TC(θ), YP(θ)), under which the agreement with

the agent’s type θ is established in its target, YP, and the transfer, TC, corresponds to the target’s

accomplishment. For this, it is necessary to guarantee that, in accepting the contract, the agent

will obtain at least the same utility it would have in autarchy—this is the well-known Restriction

of Participation (RP). This way, the principal’s problem is: C

F P P PC

PC

M P P P P P

Max Y T (Y ) N .v(Y ){Y , T }s.a: (Y T (Y ) N .Y ) N . .v(Y ) U( ) (RP)

− +

+ − + θ ≥ θ

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From RP we have that: C

P M P P P PT (Y ) U( ) Y N .Y N . .v(Y )= θ − + − θ

Soon, the government’s problem can be described as:

F M P P P P P P

P

MaxY (U( ) Y N .Y N . .v(Y )) N .v(Y ){Y }

− θ − + − θ +

A first order condition is that:

C C AP P P

1v´(Y ) Y Y

1= ⇒ >

+ θ

That is, with the transfer of funds from the federal government to the municipality being

conditioned to the attainment of a specific social target—in our case the target being an increase

in the poor’s income—we see that the final income of the poor is greater than it would have been

had there not been the establishment of targets. Without these, we see that the municipality ends

up investing the same value with or without the government’s transfer in the social area. All

transfers made the increase in the available budget for the municipality’s expenses in activities

other than in the social realm redundant, although the government would have liked to witness an

increase in these. The government would transfer resources for the municipality to use in the

social area, and the municipality would decrease in the equivalent proportion its own resources

for that area. With the establishment of targets, this seizes to happen.

Proposition 2: the establishment of social targets increases the efficiency in the use of public

money transferred to municipalities so that they can employ it in the social area, providing the

attainment of social results better than without targets.

Aside from this, in relation to the funds directed from the municipality to the social area,

we have that: TC AM M

TC TC A AM P P M P P

TC A TC AM M P P P

TC AM M

U U

G N . .v(Y ) G N . .v(Y )

G G N . .[v(Y ) v(Y )]

G G

=

⇒ + θ = + θ

⇒ = − θ −

⇒ >

Therefore, when a contract is made with social targets, the municipality, aside from

directing the resources received from government to the social area, it also increases the volume

of resources that normally it would spend if there had not been any type of contract with the

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government. It is important to observe that when there weren’t any targets, if the government had

transferred T resources to the municipality, it would have decreased by T amount its own

resources in the social area. Now, aside from not reducing any, it also increases the quantity of

its own resources to invested in the social area.

If on the one hand, the municipality loses utility from having less available funds to its

“non-social” expenses, in return it gains from the externality of improvement in the poorest’s

well-being, proportional to the investment made with the federal and municipal funds. Adam and

O’Connell (1999) also found this type of result, in which the budget destined to the poor by the

agent is greater than the funds received from the principal.

It is possible to state that a contract with social targets is capable of raising social

investments. While in the contract with no targets, the volume of resources reaching the poor

was the same with or without transfers, in this case, the one reaching the poor is greater than the

sum of the government transferred funds and those desired by the municipality in conditions

without the establishment of targets.

Impact of social targets: based on the CPO, it is possible to have an intuition about the

degree of improvement that the social targets can bring on the poor’s income. Let’s remember

that in the definition of our model, we normalized the government’s aversion to poverty as being

equal to one (θF =1). As a result of this, in the equation TCPv´(Y ) 1/(1 )= + θ , the number 1 in the

denominator is the government’s θF. If we had written the government’s utility function as UF =

GF + NP. θF. v(YP), we would have found as a first order condition:

TCP

F

1v´(Y ) =

θ + θ, where θ , is the local aversion to poverty.

Linear Contract

A way of inducing the municipality of reaching the projected targets is to offer a contract

of the type:

P PT(Y ) a b.Y= +

In this contract, the municipality has a guaranteed fixed value. It is worth observing that

this value may be positive as well as negative, implying in this last case that there is a penalty to

be paid by the municipality in case the social results are very low. We also have a variable part.

The higher the reached income, the greater the transfer. The coefficient “b,” establishing the

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value of the variable part, is know for having an incentive power, for the greater its value, the

greater is the municipality’s incentive to reach even higher social results.

Proposition 3: The coefficients belonging to a linear contract of social targets are: TC TCP Pa T(Y ) b.Y= − , onde TC TC A TC A

P P P P P PT(Y ) N .[(Y Y ) .(v(Y ) v(Y ))]= − − θ −

1b

1=

+ θ

For proof, refer to Appendix I.

3.1.5 – Favoritism without Transfer (F)

Until now, we have considered that the local government had an aversion to poverty

coefficient equal to that of all Np poor. However, there commonly exists a preference for certain

types, in detriment of others.

Empirical studies have shown that a large portion of poverty is spread among children

and teenagers. 45% of the extreme poor in Brazil have 15 years or less of age against 30% of

their share in the whole population, similar discrepancies are observed worldwide. Neri and

Costa (2001) argue that the age distribution of poverty may be influenced by the fact that the

youngest are not allowed to vote. In other words, the fact the youth is underrepresented in the

electoral market makes social expenses on children less palatable to politicians. It is not a

coincidence that family of many children and often headed by one female would be less subject

to social spending. In modern democracies, the rule that each individual gets one vote does not

apply, the rule is one adult, one vote 4 5..

Our objective is to model this type of political favoritism in relation to the determined

group and comprehend in which form it impacts the distribution of resources driven towards the

social area. In the future, we will show that the manner of establishing social targets can be of

use to diminish the problem.

Let’s make the assumption that there are two types of poor, whose populations are NP1

and NP2 for which the municipality’s aversion to poverty coefficients are θ1 and θ2, respectively.

4 Another explanation for the preference of some poor individuals is the matter of electoral region. Many politicians know they have a greater acceptance rate in a region rather than the rest, and thus they prefer to favor the place where it is easier to attain votes and support. The same occurs in relation to certain professional categories, which tend to be preferred by some politicians. 5 More generally, the sub-representation of the poor in electoral terms, would explain why fiscal spending frequently does not favor the poorest.

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Not having any type of transfer coming from the government, the municipality’s problem

can be described as:

Max GM + NP1 . θ1 . v (YP1) + NP2 . θ2 . v (YP2)

{YP1,YP2}

s.t: GM + NP1 . YP1 + NP2 . YP2 ≤ YM

The first order conditions are:

F FP1 P2

1 2

1 1v´(Y ) e v´(Y )= =

θ θ

Supposing the poor of type θ1 are preferred, that is, θ1 > θ2, we have YP1 > YP2. That is, the

preferred group receives an aid greater than the surpassed group.

3.1.6 – Favoritism Conditional on the Fulfillment of Social Targets (FC)

Let us now suppose that the main government does not have a preference for either types

of poor in a determined municipality, and that it is willing to establish with the municipality a

contract estimating a transfer of resources, TFC, linked to the attainment of certain results in the

social realm. In this case, the government’s problem is:

P1 P 2F P1 P1 P2 P2

{Y ,Y }

FCF F

FC FM P1 1 P1 P2 2 P2 M

Max G N .v(Y ) N .v(Y )

s.a: G T Y

G T N . .v(Y ) N . .v(Y ) U (RP)

+ +

+ ≤

+ + θ + θ ≥

The first order conditions are:

FCP1

1

FCP2

2

1v´(Y )

1

1v´(Y )

1

=+ θ

=+ θ

Where we conclude that: FC FP1 P1

FC FP2 P2

Y Ye

Y Y

>

>

Again, the use of a contract between the government and municipality, linking the

resource transfer to the accomplishment of social targets, causes a result better than that attained

17

without the targets. This improvement in the poor’s living conditions occurs for both types of

poor.

However, when we compare the solution attained when we had favoritism without the

existence of a contract with social targets to the situation in which there are targets, we can verify

that if type θ2 is favored for the local administration, we have that:

F FCP1 1 2 2 1 P1F FCP2 2 1 1 2 P2

v´(Y ) 1 1 1 (1 ) v´(Y )v´(Y ) 1 1 1 (1 ) v´(Y )

θ θ + θ + θ= = > = =

θ θ + θ + θ

Proposition 4: a contract with social targets would reduce the social difference among the group

less favored and the group more favored by the municipality’s social policies.

Observe the simple establishment of a contact with social targets does not guarantee that

the differences between the groups are eliminated, although they serve to soften the

discrimination problem felt by a specific group of poor. Eventually, for the two groups to have

the same results, it would be necessary for the government to consider in its utility function the

groups of poor in differentiated manners, given priority to those left behind by the municipality.

3.2 – Incomplete Information

The model with complete information is useful as a reference parameter, as it describes

the optimum solution to the problem (first-best). However, so that we have a model portraying

reality, it is interesting to soften some hypotheses. We now deal with the case where the type of

agent is private information, such that it is unknown to the principal. This is equivalent to saying

that the federal government does not know what is the local government’s aversion to poverty,

knowing only that historically there exists a specific distribution of types, with a certain

probability of the municipality being the type more or less concerned with the social issue.

We will analyze two types of cases: in one of them, we will work with the existence of

only two types of agents. In the other case, we will analyze what happens when we have infinity

of types, distributed according to a density function.

3.2.1 – Two Types of Agents

Suppose that , θ∈ θ θ and that the probability of the municipality being a type θ is π .

For the municipality to accept a contract establishing targets to be accomplished, the contract

18

must guarantee at least the same utility obtained without it. This is the Participation Restriction

(RP).

As is traditional in problems of adverse selection, the principal must offer a menu of

contracts, that is, a contract for each type of agent. The contracts must also have been chosen in a

way that the agent of a specific type does not try to pretend to be another type. This is the

Incentive Compatibility Restriction (RCI).

The principal solve the following problem:

[ ]P P

F P P F P P{Y ,T,Y ,T}

AM P P P P

M P P P P M P P P P

Max . Y T N .v(Y ) (1 ). Y T N .v(Y ) (I)

s.a:(Y T N .Y ) N . .v(Y ) U (RP )

(Y T N .Y ) N . .v(Y ) (Y T N .Y ) N . .v(Y ) (RCI )

π − + + − π − +

+ − + θ ≥ θ

+ − + θ ≥ + − + θ θ

As is commonly done, we consider the participation restriction of type θ and the

incentive compatibility restriction of type θ to be active.

(RP θ ): AM P P P PT U Y N .Y N . .v(Y )= − + − θ (*)

(*) in (RCI )θ : AM P P P P P PT (U Y ) N .v(Y ).[ ] N .Y N . .v(Y )= − + θ − θ + − θ (**)

Substituting (*) and (**) in (I) we have:

P P

AF M P P P P P P P P

{Y ,Y }

AF M P P P P P P

Max . Y [(U Y ) N .v(Y ).[ ] N .Y N . .v(Y )] N .v(Y )

(1 ). Y [U Y N .Y N . .v(Y )] N .v(Y )

π − − + θ − θ + − θ +

+ − π − − + − θ +

The first order conditions are:

P

1v´(Y )

1=

+ θ, e

P P(1 ).v´(Y ) 1 ( ).v´(Y )1

π + θ = + θ − θ − π

Remember that in the case with complete information, we had:

*P

1v´(Y )

1=

+ θ e

*P(1 ).v´(Y ) 1+ θ =

And thus, we can state that:

19

Proposition 5: with incomplete information, the poor under a government of a type more averse

to poverty are as well off as they would be with complete information. However, the poor under

a government less concerned with social issues are in a worse situation.

3.2.2 – Type Intervals

Let us consider the situation in which the municipality is of the type [ , ]θ∈ θ θ . The

municipality’s type is private information, however, the function f ( )θ is of general knowledge.

The government would like to establish a contract with the municipality where the

transfer value, T, depends on the accomplishment of certain pre-determined social targets, that is,

a contract of the type T=T(YP), assuming we are dealing with income targets, for example.

Such contract should establish differentiated targets according to the type of municipality.

As this is unknown information to the government, it is up to the government to establish

contracts (YP, T(YP)), and wait for the municipality’s choice. This is equivalent to a revelation

mechanism associating to each type announce by the municipality, a transfer ˆT( )θ for the

income target PˆY ( )θ .

The government’s problem is to determine T( )θ and PY ( )θ , for each type θ , so as to

maximize its utility, taking into consideration a distribution of types given by f ( )θ .

*P

F P PY (.),T(.)

M P P

M P P M P P

AF P P F P P

Max [G N .v(Y ( ))]dF( )

s.a: G ( ) N . .v(Y ( )) U( ) [ , ] (RP )

ˆ ˆ ˆG ( ) N . .v(Y ( )) G ( ) N . .v(Y ( )) (RCI )

Y T( ) N .v(Y ( )) Y N .v(Y ( )

θ

θ+ θ θ

θ + θ θ ≥ θ ∀θ∈ θ θ θ

θ + θ θ ≥ θ + θ θ ∀θ ≠ θ θ

− θ + θ ≥ + θ

∫

) (RPGoverno)

The first restriction states that municipalities will only agree to a contract with the

government if the utility derived from the contract is greater than or equal to the saved utility,

which would be obtained if there had not been any contract, that is, in autarchy.

The second restriction guarantees the municipality the utility obtained when revealing

that its true type θ is greater than that it would have obtained in case it had identified itself as

being another type θ̂ . This is the well-known Incentive Compatibility Restriction of type θ.

The third and last restriction is so that the government can identify with which

municipalities it is worth to establish a contract. It guarantees that the government’s utility in

20

carrying out the contract will be greater than if there had not been one. Nothing guarantees that it

will be favorable for the principal (government) to establish a contract with all agents

(municipalities), when there are an infinite number of types. In relation to the municipalities

with low adversity to poverty, it maybe happen that it is not favorable for the government to

perform transfers, for the municipality would invest a small amount in social programs, when

compared to other municipalities more adverse to poverty. The type *θ identifies the limit from

which it is interesting for the government to transfer resources or not. This characteristic within

the contract allows us to state that:

Proposition 6: the municipalities experiencing a more intense poverty—due to the low aversion

to poverty by their local governments—can be impeded of signing contracts of social targets and

thus be kept from receiving government funds.

This is a controversial result, since where the government is expected to intervene is

actually the place where it should pass on the responsibility. As in the case of unconditional

transfers, what happens is that in these municipalities the transfers performed by the government

to the municipality almost does not change the poor’s situation, since the municipality tends to

reduce the channeling of its own resources to the social realm in a quantity almost equivalent to

that received from the government 6.

Taking into consideration the definitions of GF, GM and U( )θ , we can rewrite the

equation of maximizing the government as:

*P

F P PY (.),T(.)

A AM P P P P M P P P P

M P P P P M P P P P

F P P

Max [Y T( ) N .v(Y ( ))]dF( )

s.a: [Y T( ) N .Y ( )] N . .v(Y ( )) [Y N .Y ( )] N . .v(Y ( ))

ˆ ˆ ˆ[Y T( ) N .Y ( )] N . .v(Y ( )) [Y T( ) N .Y ( )] N . .v(Y ( ))

Y T( ) N .v(Y (

θ

θ− θ + θ θ

+ θ − θ + θ θ ≥ − θ + θ θ

+ θ − θ + θ θ ≥ + θ − θ + θ θ

− θ + θ

∫

AF P P)) Y N .v(Y ( ))≥ + θ

Defining the municipality of type θ ’s utility upon announcing itself as type θ̂ and choosing a

contract Pˆ ˆ(Y ( ), T( )θ θ ), as ˆV( , )θ θ , we have that:

M P P P Pˆ ˆ ˆ ˆV( , ) [Y N .Y ( ) T( )] N . .v(Y ( ))θ θ = − θ + θ + θ θ

6 In practice, this problem is softened since part of the investments in the social area (education, health, social services, etc) has a minimum percentage linked to the local budget—refer to the Fis cal Responsibility Law and the Federal Constitution. This way, when the budget increases, the municipality is forced to increase its total expenses in these areas, incapable of simply using the federal funds and reducing the local ones by an equivalent amo unt.

21

and defining V( )θ as the utility from revealing its true type :

M P P P PV( ) V( , ) [Y N .Y ( ) T( )] N . .v(Y ( ))θ = θ θ = − θ + θ + θ θ

This way, we can redefine the government’s problem as:

*P

F M P P P P P PY (.),V(.)

AF M P P P P P P F P P

Max {[Y V( ) Y N .Y ( ) N . .v(Y ( ))] N .v(Y ( ))}dF( )

s.a: V( ) U( ) [ , ] (RP )

ˆ ˆV( , ) V( , ) (RCI )

Y [V( ) Y N .Y ( ) N . .v(Y ( ))] N .v(Y ( )) Y N .v(Y ( ))

θ

θ− θ + − θ + θ θ + θ θ

θ ≥ θ ∀θ∈ θ θ θ

θ θ ≥ θ θ ∀θ ≠ θ θ

− θ − + θ − θ θ + θ ≥ + θ

∫

Solving the following equation, we have that:

Proposition 7: the optimum contract to be established between the government and a

municipality of type *θ ≥ θ , given that d 1 F( )

0dx f( )

− θ≤ θ

, may be characterized by:

a) P

1 F( )(1 ) .v´(Y ( )) 1

f ( ) − θ

+ θ − θ = θ

b) *M P P P PT( ) V( ) Y N .Y ( ) N . .v(Y ( )) [ , ]θ = θ − + θ − θ θ ∀θ∈ θ θ

where *

*P PV( ) N .v(Y ( )).d U( )

θ

θ

θ = θ θ + θ∫ , and the coefficient *θ ’s value is determined by the

government’s Participation Restriction

Proof: Appendix II

4 – Dynamic Model

One of the important aspects to be considered in contractual relations is the temporal

dimension. Contracts are established and have deadlines for various periods—in general7. Up

until now, we had analyzed only static contracts, observed only throughout one period. The

objective in this chapter is to study the modifications occurring in our model when we deal with

relations lasting over one period. We wish to know what type of contract should the government

establish with the municipality having in mind long run actions, which could correspond to

various term years, or even various terms.

7 The definition of what is a period depends upon the situation; it can correspond to a month, a year, a mandate, a generation, etc.

22

We will support ourselves primarily based on the presentation regarding dynamic models

made by Salanié (1997). We see that the results in the dynamic case are often contrary to what

we would have expected in a more superficia l analysis. In some cases, we limit ourselves to

showing the result’s subjacent intuition, without presenting a formal development, in light of the

complexity of the dynamic models.

We restrict our analysis to complete contracts. These, according to Salanié, are those in

which “all variables which may have an impact on the contractual relations’ conditions,

throughout its entirety, were taken into account at the moment of negotiation and the signing of

the contract. This way, the contract should be contingent upon a large number of variables. This

hypothesis implies that none unexpected situation appears during the contractual relation: any

shift in the economic environment has as its only implication the implementation of a pre-

established rule of the cont ract.”

The hypothesis of complete contracts is relatively strong, although it displays the

advantage of being reasonably studied. At the end of this chapter, we write a brief explanation

for the implications of having incomplete contracts.

Commitment and renegotiation are two key concepts to our analysis. According to Salanié

(1997), commitment refers to the agent’s ability to restrict beforehand its future actions through

the promise of maintaining the contract during an agreed period. The length of commitment

determines the contract’s strictness; the longer the length of the agent’s commitment, the stricter

the contract. An agent’s commitment depends upon a series of factors, such as:

• agent credibility: the greater the importance of an agent’s reputation, the greater will be

his commitment in keeping the contract, aiming to maintain or increase his reputation;

• legal framework supporting the contracts: establishes punishments and fines in case of a

contract breach;

• contractual penalizations: should be applied, according to contract, in case it is breached

unilaterally.

In counterpart to commitment, we have renegotiation and unilateral breach of contract.

Renegotiation refers to the decision taken in overall agreement, bilateral or multilateral, of not

fulfilling the contract terms previously agreed upon. The unilateral decision occurs when an

agent does not keep the deal, without the attainment of any type of agreement from the other

entities. Such a decision may lead to a fine, which does not occur in the previous case.

23

There are three distinct cases of what compromises the issue:

• Full Commitment: the contract establishes the rules enduring throughout its lifetime,

when there is not the possibility of any type of renegotiation among the parties, even if

they agree about a change. Suppose, for example, that the contract involves three or more

entities, and if two of them have the possibility of obtaining a mutual improvement in

case there is a renegotiation. Even if this renegotiation does not worsen the sit uation of

other entities, nonetheless it will not be allowed in a full commitment contract.

• Long term commitment 8: the contract establishes rules for all periods of its lifetime,

however, having the possibility that the contract’s members renegotiate their relations.

Such a renegotiation is only possible if both parties are in agreement, not being

permissible that one imposes upon the other a new contract. This type of contract is also

known as long-term commitment with renegotiation.

• No commitment or spot commitment: the contract establishes rules for the first period. In

relation to the following periods, the parties may choose to sign a new contract with the

same terms, different terms, or not sign a contract at all.

The issue of whether or not there exists commitment and the possibility for renegotiation

among agents is fundamental in the analysis of complete dynamic contracts. Still referring to

Salanié (1997), a final result in the theory of individual choices is that no agent, alone, can

improve its situation by having its choice possibility limited. When there is a greater number of a

choice restriction, the final result tends to be worsen—it might be the same, but never better.

Such a result is not valid when there is interaction among agents. As an illustrative example, we

have the Prisoner’s Dilemma. The prisoners may declare themselves guilty or innocent and the

resulting Nash equilibrium is that both declare themselves to be guilty. However, if both had

committed to declare themselves as innocent, the result would be better for both. This shows that

the existence of a commitment mechanism—implying a limitation in the prisoners’ choice—

would cause them to be better. The lack of commitment by the agents, however, becomes

harmful to both. In relation to our model’s dynamic contracts, we see the same principal being

valid in the relationship between the government and municipalities.

8 Dewatripont (1989) introduced the concept of long-term commitment.

24

4.1 – Full Commitment

Again suppose that the government is in a situation of incomplete information. Suppose

that the government is in a situation of incomplete information, in which the type of the

municipal administration with which it intends to establish a contract of social targets is

unknown. The government knows there are two available types, θand θ , and the probabilities

associated to each type are (1-π) and π , respectively. This same problem was dealt with

previously. Let’s consider that the contract to be established between the government and the

municipality has a due date of T periods instead of only one period (static case). Such contract

cannot be renegotiated by any of the entities, be it unilaterally or bilaterally, even if such

negotiation is consensual among them. In each period, the government takes on the commitment

of performing a transfer T, for the municipality to invest in the social area, which is responsible

for reaching a social target within each period.

The government’s utility throughout the contract’s lifetime is

t t

Tt 1

F F t P Pt 1

U (Y T ) N .v(Y )−

=

= δ − +∑

and that of the local government is given by:

t t t

Tt 1

M M t P P P Pt 1

U (Y T N .Y ) N . .v(Y )−

=

= δ + − + θ∑

where δ is the inter-temporal discount factor, considered constant throughout time and the same

for both government and municipality.

According to Salanié (1997), having total commitment, the revelation principle is valid

in the dynamic case, for all parts interested in the contract negotiate once, when there are not

types of alteration in the agreement.

This way, the government’s problem is to propose, for each possible type of municipality,

a sequence of targets and transfers for each contract year. It is the municipality’s responsibility to

announce itself as being θ or θ and sign the contract for its type. The government’s problem,

however, is to choose the sequence t t

TP t P t t 1{Y ( ),T( ),Y ( ) ,T( )} =θ θ θ θ that maximizes its utility and

that fulfills the restrictions of incentive compatibility and of municipal participation, such that it

announces its true type.

In formal terms, the government’s equation is given by:

25

T t t t tP t P t t 1t t

t t t

t t t

T Tt 1 t 1

F t P P F t P P( Y , T , Y , T ) t 1 t 1

Tt 1

M t P P P Pt 1

Tt 1

M t P P P Pt 1

Max . (Y T ) N .v(Y ) (1 ). (Y T ) N .v(Y )

s.a: (RP ) .[(Y T N .Y ) N . .v(Y )] U( )

(RP ) .[(Y T N .Y ) N . .v(Y )] U( )

(

=

− −

= =

−

=

−

=

π δ − + + − π δ − +

θ δ + − + θ ≥ θ

θ δ + − + θ ≥ θ

∑ ∑

∑

∑

t t t t t t

t t t t t t

T Tt 1 t 1

M t P P P P M t P P P Pt 1 t 1

T Tt 1 t 1

M t P P P P M t P P P Pt 1 t 1

RCI ) .[(Y T N .Y ) N . .v(Y )] .[(Y T N .Y ) N . .v(Y )]

(RCI ) .[(Y T N .Y ) N . .v(Y )] .[(Y T N .Y ) N . .v(Y )]

− −

= =

− −

= =

θ δ + − + θ ≥ δ + − + θ

θ δ + − + θ ≥ δ + − + θ

∑ ∑

∑ ∑

The solution to this equation allows us to establish that:

Proposition 8: having total commitment, the government must establish as target to be reached

by the municipality, the same that would be established in the static case (one period). This

target must be maintained throughout the contract’s lifetime—during T periods. The optimum

contract has the following sequence of targets and transfers:

t t

T TP t P t t 1 P P t 1{Y ( ),T( ),Y ( ) ,T( )} {Y ,T,Y ,T}= =θ θ θ θ =

where P P{Y,T ,Y ,T} is the solution to the static case.

Proof: Appendix III

The process occurs as if an optimum contract for a single period had been established and

this contract had been continuously renewed during T periods. Some possible interpretations for

this result are:

a) If the target YP is an income target, the government’s objective should be to establish

minimum income, P PY eY —which should be reached by the first year—for each type of

municipality, transferring T e T each year, as a way of maintaining the minimum income.

b) If the target YP is seen as a percentage variation—for example, the reduction of infant

mortality rate, the increase in school attendance—the government’s objective becomes

the attainment of a continuous variation over the chosen social indicator, such that period

after period, it is the same as the one obtained in the first period.

Figure 1 below displays the solution to the problem when we have a contract expanding over

only two periods.

26

Figure 1

The problem of total commitment contracts is how to guarantee that there are not bilateral

negotiations taking place. In our case, after the initial period, the municipalities reveal their types

and the government starts to have an incentive to propose a renegotiation with some

municipalities. We cannot forget that, due to the asymmetry of information, the contract

established between the government and the municipality of type θ, P(Y ,T) , is done so in a way

that the municipality has as its target a value lower than that established by complete information *

P PY Y< . This causes an inefficient allocation of public resources. Since part of the informational

asymmetry disappears after the first period, the government would like to propose to the

municipality of type θ, in the second period, an optimum contract ( * *PY , T ).In this type of

contract, the municipality has a higher target to accomplish and would receive more resources to

do so, such that its utility would remains the same. However, the government would be better off

and so would the poor. This type of reasoning suggests that the establishment of a contract with

total commitment consequently has ex-post inefficiency, in light that the entities are kept from

renegotiating among themselves. What would occur if this possibility were allowed? That is

what we will determine in the following item.

4.2 – Long Term Commitment

Let’s suppose that the only difference to the previous case is that we deal with a two-

period dynamic contract, instead of T periods9. Besides, we have the possibility of a bilateral or

multilateral renegotiation, if there is a consensus among the parties, since the contract is a long-

term commitment one.

9 Due to the complexity of the dynamic problem, we use the usual approach, which consists in analyzing the problem with two periods.

27

In this situation, the government knows the type of each municipality after the first

period, in accordance to the chosen contract. However, there is a problem of complete

information for the second period, in which the government would like to establish new contracts

with all municipalities, using the information it has acquired about each one. It would be ideal

for the government to establish an optimum contract (first-best) in the second period. However,

with this type of contract, the municipality of type θ would experience a loss in utility. As has

been stated, one of the conditions so that renegotiation occurs is that both parties are in

agreement. Obviously the municipality of type θ would not agree to renegotiate its contract if

that meant establishing an optimum contract for the government.

In relation to the municipality of type θ, if the government offered an optimum contract,

the municipality would not be better nor worse—remember that in both the optimum contract

and in the one with incomplete information, the municipality of type θ has the same utility

(reserved utility) as obtained in autarchy. This way, the municipality would be willing to accept

the new contract, resulting in amelioration for the government and the poor. In this situation,

however, there would be incentive so that a renegotiation would occur between the government

and the municipality of type θ.

At first sight, the contract with long-term commitment allows for a gain in efficiency in

the use of public money. Such a conclusion, however, is not so simple. Let’s understand why.

As observed in the problem with two types of municipalities and incomplete information,

the municipality of type θ has a likelihood of pretending to be of type θ, So that this does not

occur, the government maximizes its utility subject to incentive compatibility restrictions, and

proposes a menu of contracts so that the municipalities reveal their true type. The solution to the

problem implies that the municipality θobtains an informational income and is indifferent

between a contract of its type and of type θ—we suppose that when the municipality is

indifferent, it chooses the contract for its type. Another characteristic of this menu is that

municipality θ obtains a contract in which it must reach a target below the optimum target, for if

a contract were offered in which municipality θ had to reach the optimum target, then the

municipality θ would pretend to be of type θ.

In the dynamic case, we see that it is advantageous for the government to renegotiate with

municipality θ in the second period, and offer an optimum contract. What happens is that

28

municipality of type θ , knowing that there is such a possibility in the second period, prefers to

pretend to be of type θ in the first period. The reason for this is that:

• In relation to the first period, its utility will not change.

• In the second period, however, its utility will increase. In the beginning of the second

period, the government will think that it’s of type θ and will propose a contract

renegotiation, offering an optimum contract for type θ. This contract, as explained,

provides a greater utility than that obtained with the contract offered to type θ in the first

period.

The result is that the government, by establishing a contract allowing renegotiation,

motivates the municipalities of type θ to not reveal its type and to make themselves pretend to

be less concerned with poverty, θ. This creates a hardship in the choice of municipalities θ of

contracts having modest social targets than those they would have chosen had they known there

would not be a renegotiation between the government and municipalities of type θ. Therefore,

what appears to be a solution to increase the efficiency of public funds, ends up being a source of

greater inefficiency.

A contract with full commitment is inefficient ex-post to the government when

comparing with the long-term commitment contract, since the government does not use the

information obtained from the first period in the second period. However, the long-term

commitment contract is inefficient ex-ante in relation to the full commitment one, for as long as

there is no commitment, the final result is worse for the government.

What the theory shows us is that to find a solution to the contract with long-term

commitment it is necessary to consider, in the formulation of the problem, the possibility of

renegotiation. This is done through the inclusion of additional restrictions, known as sequential

efficiency restrictions or non-renegotiation restrictions. This denomination occurs due to the fact

that solutions obtained with these restrictions imply that there is no renegotiation during the

contract’s lifetime. Any possible renegotiation is anticipated and considered at the moment of the

contract’s elaboration.

Solutions of this type are extremely complex. Due to this, we base ourselves on articles

dealing with similar problems to derive the type of solution we might find in our model. Hart-

Tirole (1988) and Laffont-Tirole (1990)—considering a contract with two periods—solve the

29

problem of dynamic long-term commitment contracts in different contexts. In the solutions

found, in the first period, agents of type θ split. One part, 1-x, reveals its type, while the other, x,

pretends to be θ. For those revealing their type, the principal offers an optimum contract with

incomplete information P(Y , T ) . In the second period, the agents of type θ pretending to be θ,

reveal their type, renegotiate the contract and sign the same type of contract P(Y , T ) as other

agents of type θ had already signed in the first period.

Following, in figure 2, we illustrate the type of solution found in the cited articles. In our

case, considering the probability that the municipality is of type θ is π and that the portion of

municipalities not revealing their type is x, then at the beginning of the second period, the

probability of a municipality being of type θ (in case it had identified itself as θ in the first

period) is:

)1(..

2 πππ

π−+

=x

x

Considering that the second period is also the last, the solution in this period is

determined as the solution to the static problem. This way, the contract offered to the type θ in

the second period is equal to the solution to the problem with two types of municipalities and

incomplete information. The only thing needed is to substitute the probability π for the

probability π2 in the first order condition determined by that case. The FOC attained in the

second period is:

[ ])´().(1

1)´().1(2

2PP YvYv θθ

ππ

θ −+

+=+

Given that ππ >2 we have that:

PP YY >2

We see, however, that the possibility of the government to renegotiate—with a

municipality of type θ—the contract in the second period, implies in a solution with higher

targets for these municipalities. Having in mind the targets as the poor’s income, there is an

increase in the poorest’s income. This does not mean an increase in the efficiency of the public

money use, since part of municipalities θ pretends to be of type θ and reaches lower targets in

30

the first period that in case of full commitment. Besides, the targets of type θ in the first period

are lower than they would have been with full commitment.

Figure 2

4.3 – Non-commitment

In this case, the government does not have the commitment to maintain in the second

period the contract established in the first. In a long-term commitment contract, if the

municipality of type θ revealed its type in the first period, it would have ensured in the second

period the same contract as in the previous period. This would then guarantee an informational

income equal to that in the first period, since the government would be unable to use the

information obtained to impose a renegotiation implying losses for the municipality.

In the case of non-commitment, the government, once aware of the type of municipality,

is not obliged to repeat in the second period the initial contract. More than this, it can use the

information attained in the first period and offer an optimum contract (first-best) as the only

alternative to the municipality of type θ . This implies that the municipality of this type attains an

informational income equal to zero in the second period and a utility equal to that obtained in

autarchy. Due to this possibility, the municipality of type θ prefers to identify itself as being θ in

the first period. In this case, its utility in the first period does not change—having the same

informational income it would have had it identified itself as θ --and it may acquire an

informational income also in the second period, having seen that the government remains not

knowing its type. As a result, in this type of contract, inefficiency is even greater than the long-

term commitment, since the incentive for the municipality of type θ to choose the contract of

type θ are even greater than in the previous case.

31

In the case in which the government has the freedom of making total use of all the

information attained in the first period, the result is the worst possible, since the municipality of

type θdoes everything in its power so as to not reveal any information, or reveal information in

the slowest manner possible. This is the known ratchet effect, for once the municipality reveals

any information regarding its type, it permanently loses the possibility of having some sort of

informational income with this information, being unable to turn back time.

To avoid that the municipality θ identifies itself as θ, the government must anticipate—

in the first period—all expected value for informational income that θmight obtain in the future

had there been a commitment, discounting according to the parameter d. The problem with this

type of solution is that the help given in the first period to those identifying themselves θ as can

be so high that it induces the municipality of type θ to pretend to be θ . So that this does not

occur, the government must find a gray area, so that in a contract with T periods, the

municipality slowly reveals its type.

Problems of this type are extremely difficult to solve. We will restrain ourselves only in

the explanation for the intuition. As Salanié (1997) summarizes, the velocity of revealing the

type depends primarily on the parameters d e T. In a situation where the mandate is almost

over—when the mayor is not concerned with the future or has a low commitment to the future

administration—we have a situation with a low d or even equal to zero. In this case, the velocity

of revealing information is high. In the opposite case—the beginning of a term—an agreed

contract with the possibility of being renewed throughout the term, causes the municipality to

slowly reveal its type10.

The situation without any type of commitment displays slower velocity of type

revelation, which implies a greater inefficiency in the allocation of public resources.

Summarizing the issue of dynamic problem, we have that:

Proposition 9: In a situation with full contracts and incomplete information, the best the

government can do to increase the efficiency of public funds is to offer an optimum contract with

incomplete information throughout the course of contract’s duration, creating institutional

mechanisms guaranteeing the impossibility of bilateral negotiations.

10 Laffont-Tirole (1987) analyzed the comparative statistic of optimum contracts in the case of dynamic incentives.

32

4.4 – Incomplete Contracts

In the prior section, we concluded that under the hypothesis of full contract, the ideal is

that the government establish a pact with all participating municipalities, so that during the

social target contract’s lifetime, there is not the possibility of the government bilaterally

renegotiating the targets with some municipalities. Such as would occur in the Prisoner’s

Dilemma, the alternatives’ restriction imposed by full commitment allows for a Pareto

improvement in relation to other solutions.

However, this conclusion remains invalid in the case where we have incomplete contracts.

This is an important implication, since the hypothesis of full contracts is relatively strong. In the

real world, there are a series of problems to attain a full contract:

• The elaboration of a contract has expenses. In some situations, the cost of contemplating

an unlikely situation can be greater than the benefit of farseeing what to do in that

situation;

• In some contingent state, the verification of the values taken on by relevant variables is

difficult or impossible. It does not allow for a mediation of disputes potentially arising;

• There is a problem of limited rationality which makes the agents unaware of the proper

knowledge to precisely evaluate the impact of some variables;

• There is a difficulty and even impossibility in attributing probabilities for every natural

state.

In the previous case, the possibility of renegotiation created ex-ante inefficiencies.

Meanwhile, in this situation, the renegotiation functions as a means of treating the cases

unpredicted in the contract, which could bring social gains.

5 – Conclusion

This paper discussed the economic rationality of a system of social targets based on

international Millenium Development Goals (MDGs), as a way for the federal government to

increase efficiency in the use of its social budget transferred to municipalities. The paper

developed extensions of a standard principal-agent framework in various directions. The results

of the static models show that the use of the focalization criteria where the poorest municipalities

get more resources may lead to adverse incentives to poverty eradication. We also show that

unconditional transfers from the federal government totally crowd-out local social expenditures.

33

The paper argues in favor of the use of contracts where the greater the improvement in relevant

social indicators, the more resources each municipality would receive. The introduction of

imperfect information basically generates a penalty to the poor segments in areas where local

governments are less averse to poverty.

An advantage of this type of contract is also to reduce the problem of political favoritism

when certain social groups receive greater, or smaller, attention from specific governments. With

the establishment of social targets it becomes possible to generate proper incentives so that social

spending is distributed more equitably between groups.

6 –References

• Adam, C.S., O’Connell, S.A. (1999). Aid, Taxation and Development, in Sub-Saharan

Africa. Economics and Politics 11: 225-253

• Azam, J.P., Laffont, J.J. (2001). Contracting for aid. Mimeo, Université de Toulouse.

• Besley, T. (1997). Political Economy of Alleviating Poverty: Theory and Institutions.

Annual World Bank Conference on Development Economics 1996, World Bank:

Washington, D.C.

• Dewatripont, M. (1989). Renegotiaton and Information Revelation over Time: The Case

of Optimal Labor Contracts. Quarterly Journal of Economics, 104: 589-619.

• Gelbach, J.B., Pritchett, L.H. (1997). More for the poor is less for the poor. Policy

Research Working Paper 1799, World Bank: Washington, D. C.

• Hart, O., Tirole, J. (1988). Contract Renegotiation and Coasian Dynamics. Review of

Economic Studies, 55: 509-40.

• Hoffmann, R. (1998). Distribuição de Renda: Medidas de Desigualdade e Pobreza. São

Paulo: EDUSP.

• Laffont, J.J, Tirole, J. (1987). Comparative Statistics of the Optimal Dynamic Incentives

Contract. European Economic Review, 31: 901-26.

• Laffont, J.J, Tirole, J. (1988) "The dynamics of Incentive Contracts". Econometrica,

Setembro, Vo156 (5), págs 1153-1175.

• Laffont, J.J, Tirole, J. (1990). Adverse Selection and Renegotiation in Procurement.

Review of Economic Studies, 75: 597-626.

34

• Laffont, J.J, Tirole, J. (1993). A Theory of Incentives in Procurement and Regulation.

Cambridge: MIT Press.

• Laffont, J.J., Tirole, J. (1998). The Dynamics of Incentive Contracts. Econometrica, 56:

1153-1173.

• Mas-Colell, A., Whinston, M.D., Green, J.R., Microeconomic Theory, Oxford University

Press, (1995)

• Meyer,M.A., Vickers,J. (1997) "Performance Comparisons and Dynamic Incentives".

Journal of Political Economy, Vo1105, No.3, Junho, pags 547-581

• Neri, M.C. et all. (1999) “Gasto Público en Servicios Sociales Básicos en América Latina

y el Caribe: Análisis desde la perspectiva de la Iniciativa 20/20” (pelo PNUD, CEPAL

(Nações Unidas) e UNICEF, organizado por Enrique Ganuza, Arturo Leon e Pablo

Sauma, Santiago, Chile, Outubro.

• Neri, M.C. (2000) “Metas sociais, para tirar a miséria do país”, Revista

ConjunturaEconômica, Maio.

• Neri, M.C., Costa, D. O Tempo das Crianças”, Cadernos Adenauer – As Caras da

Juventude, N.º 06, Ano II, pp. 65 à 86, Rio de Janeiro, 2001.

• Neri, M.C. e Xerez M. C. (2003), Desenho de Um Sistema de Metas Sociais, Anais da

Anpec, Porto Seguro, Bahia, Dezembro e Ensaios Econômicos Nº 519, EPGE / FGV, Rio

de Janeiro, dezembro de 2003.

• Neri, M.C. e Xerez M. C. (2003), Aspectos Dinâmicos de um Sistema de Metas Sociais,

Anais da Anpec, João pessoa, Dezembro e Ensaios Econômicos Nº 563, EPGE / FGV,

Rio de Janeiro, dezembro de 2004.

• PNUD. (1998). Desenvolvimento Humano e Condições de Vida: Indicadores Brasileiros.

• Salanié, B. (1997). The Economics of Contracts. Cambridge: MIT Press.

35

Appendix I – Proposition 3

So that the poor experience an increase of one unit in income, it is necessary that the

municipality spend NP.1 in the social project. According to the targets’ contract, for each unit of

increase in the poor’s income, the government transfers to the municipality b.NP in funds. The

liquid result is a variation on the local available budget for increment unit in the poor’s income:

MP p

P

Gb.N N

Y∆

= −∆

(*)

The governmet’s utility function: C

F F P P PU Y T (Y ) N .v(Y )= − +

From the municipality’s budgetary restriction (RO), we have: C

M P M P PY T (Y ) G N .Y+ = +

Isolating TC(YP) in RO and substituting the government’s utility function, we have that:

M F F M P P P PG (Y U Y ) N .Y N .v(Y )= − + − +

In optimum, we have:

TC TCMP P P P

P

dG 1N N .v´(Y ) onde, v´(Y )

dY 1= − + =

+ θ

Thus,

MP P

P

dG 1N N .

dY 1= − +

+ θ (**)

From (*) and (**) we have:

P p P P

1 1b.N N N N . b

1 1− = − + ⇒ =

+ θ + θ

In relation to the coefficient “a”, we have: TC TCP P

TC TCP P

T(Y ) a b.Y

Logo,

a T(Y ) b.Y

= +

= −

Being that

TC TC TC A TC AP P P P P P P

1 1b , v´(Y ) , T(Y ) N .[(Y Y ) .(v(Y ) v(Y ))]

1 1= = = − − θ −

+ θ + θ

36

Appendix II – Proposition 7

The government’s problem is:

*P

F M P P P P P PY (.),V(.)

AF M P P P P P P F P P

Max {[Y V( ) Y N .Y ( ) N . .v(Y ( ))] N .v(Y ( ))}dF( )

s.a: V( ) U( ) [ , ] (RP )

ˆ ˆV( , ) V( , ) (RCI )

Y [V( ) Y N .Y ( ) N . .v(Y ( ))] N .v(Y ( )) Y N .v(Y ( ))

θ

θ− θ + + − θ + θ θ + θ θ

θ ≥ θ ∀θ∈ θ θ θ

θ θ ≥ θ θ ∀θ ≠ θ θ

− θ − + θ − θ θ + θ ≥ + θ

∫

Analyzing the incentive compatibility restriction, we see that the for the local utility to be

maximum when revealing its true type, it is necessary that:

2

2ˆ ˆ

ˆ ˆV( , ) V( , )0 e 0ˆ ˆ

θ=θ θ=θ

∂ θ θ ∂ θ θ= ≤

∂θ ∂θ

Considering that: M P P P Pˆ ˆ ˆ ˆV( , ) [Y N .Y ( ) T( )] N . .v(Y ( ))θ θ = − θ + θ + θ θ

P P P P P

ˆV( , ) ˆ ˆ ˆ ˆN .Y ´( ) T´( ) N . .v´(Y ( )).Y ´( )ˆ∂ θ θ

= − θ + θ + θ θ θ∂θ

(1)

2

P P P P P P P P2

ˆV( , ) ˆ ˆ ˆ ˆ ˆ ˆ ˆN .Y ´́ ( ) T´́ ( ) N . .[v´´(Y ( )).Y ´( ).Y (́ ) v´(Y ( )).Y ´́ ( )]ˆ∂ θ θ

= − θ + θ + θ θ θ θ + θ θ∂θ

(2)

Therefore,

P P P P Pˆ

ˆV( , )0 T´( ) N .Y ´( ) N . .v´(Y ( )).Y (́ )ˆ

θ=θ

∂ θ θ= ⇒ θ = θ − θ θ θ

∂θ (3)

22

P P P P P P P2ˆ

ˆV( , )0 T´́ ( ) N .Y ´́ ( ) N . .[v´´(Y ( )).(Y ´( )) v´(Y ( )).Y ´́ ( )]ˆ

θ=θ

∂ θ θ≤ ⇒ θ ≤ θ − θ θ θ + θ θ

∂θ (4)

Deriving (3) in relation θ we have: 2

P P P P P P P P P P

lado direito da equação (4)

T´́ ( ) N .Y ´́ ( ) N . .[v´´(Y ( )).(Y (́ )) v´(Y ( )).Y ´́ ( )] N v´(Y ( )).Y ´( )θ = θ − θ θ θ + θ θ − θ θ1444444444442444444444443 (5)

Substituting (5) in (4):

P P P P PT´́ ( ) T´́ ( ) N .v´(Y ( )).Y (́ ) v´(Y ( )).Y ´( ) 0θ ≤ θ + θ θ ⇒ θ θ ≥

Given that Pv´(Y ( )) 0θ ≥ and thus

PY (́ ) 0θ ≥ (4´)

37

It was defined that: M P P P PV( ) [Y N .Y ( ) T( )] N . .v(Y ( ))θ = − θ + θ + θ θ . Deriving this

equation in relation to θ we have:

P P P P P P PV´( ) N .Y ´( ) T (́ ) N .v(Y ( )) N . .v´(Y ( )).Y ( )θ = − θ + θ + θ + θ θ θ ⇒

P P P P P P P

lado direito da expressão (3)

T´( ) V´( ) N .v(Y ( )) N .Y (́ ) N . .v´(Y ( )).Y ( )θ = θ − θ + θ − θ θ θ144444424444443 (6)

Substituting (6) in (3):

P PV (́ ) N .v(Y ( ))θ = θ (3´)

However, the incentive compatibility restriction of a municipality of type θ (RCI θ ) can

be substituted by the equations (3´) and (4´) in the government’s problem.

The government’s problem with the new restrictions is:

*P

F M P P P P P PY (.),V(.)

P

P P

AF M P P P P P P F P P

Max {[Y V( ) Y N .Y ( ) N . .v(Y ( ))] N .v(Y ( ))}dF( )

s.a: V( ) U( ) [ , ] (RP )

Y ´( ) 0

V (́ ) N .v(Y ( ))

Y [V( ) Y N .Y ( ) N . .v(Y ( ))] N .v(Y ( )) Y N .v(Y ( ))

θ

θ− θ + + − θ + θ θ + θ θ

θ ≥ θ ∀θ∈ θ θ θ

θ ≥

θ = θ

− θ − + θ − θ θ + θ ≥ + θ

∫

The equation’s Hamiltonian is given by:

F M P P P P P P P PH [Y V( ) Y N .Y ( ) N . .v(Y ( ))] N .v(Y ( ))].f( ) ( ).N .v(Y ( ))= − θ + + − θ + θ θ + θ θ + µ θ θ

H(́ ) f( ) (́ ) (u).du f(u).du ( ) ( ) F( ) F( )

V

θ θ

θ θ

∂= − µ θ ⇒ θ = µ θ ⇒ µ = ⇒ µ θ − µ θ = θ − θ

∂ ∫ ∫

Considering that for θ the restriction is inactive, ( ) 0µ θ = , and thus

( ) (1 F( ))µ θ = − − θ (9)

P P P P P P PP

H0 [ N N . .v´(Y ( ))] N .v´(Y ( ))].f( ) ( ).N .v´(Y ( )) 0

Y∂

= ⇒ − + θ θ + θ θ + µ θ θ = ⇒∂

Pv´(Y ( )).[(1 ).f( ) ( )] f ( )θ + θ θ + µ θ = θ (10)

Substituting (9) in (10):

P1 F( )

v´(Y ( )). (1 ) 1f ( )

− θθ + θ − = θ

38

b) The equation for the value to be transferred from the government to the municipality is

obtained from the definition of V( )θ :

M P P P PV( ) [Y N .Y ( ) T( )] N . .v(Y ( ))θ = − θ + θ + θ θ ⇒

M P P P PT( ) V( ) Y N .Y ( ) N . .v(Y ( ))θ = θ − + θ − θ θ

To obtain V( )θ take the integral of (3´):

* * *

* * *P P P PV´(u).du N .v(Y (u)).du V( ) V( ) N .v(Y (u)).du / V( ) U( ) /

θ θ θ

θ θ θ

= ⇒ θ − θ = ⇒ θ = θ ⇒∫ ∫ ∫

**

P PV( ) N .v(Y ( )).du U( )θ

θθ = θ + θ∫

Appendix III – Proposition 8

t t

TP t P t t 1M {Y ( ),T( ),Y ( ) ,T( )} == θ θ θ θ is the solution to the government’s equation in the dynamic

situation. Such optimum mechanisms should fulfill the incentive compatibility restrictions and

the municipality’s participation, that is:

t t

t t

T Tt 1 t 1

M P P t P Pt 1 t 1

T Tt 1 t 1

M P P t P Pt 1 t 1

.[Y N .Y T N . .v(Y )] .U( ) (RP )

.[Y N .Y T N . .v(Y )] .U( )

− −

= =

− −

= =

δ − + + θ ≥ δ θ θ

δ − + + θ ≥ δ θ

∑ ∑

∑ ∑

t t t t

t t t t

T Tt 1 t 1

M P P t P P M P P t P Pt 1 t 1

T Tt 1 t 1

M P P t P P M P P t P Pt 1 t 1

(RP )

.[Y N .Y T N . .v(Y )] .[Y N .Y T N . .v(Y )] (RCI )

.[Y N .Y T N . .v(Y )] .[Y N .Y T N . .v(Y )] (RCI

− −

= =

− −

= =

θ

δ − + + θ ≥ δ − + + θ θ

δ − + + θ ≥ δ − + + θ θ

∑ ∑

∑ ∑ )

We now consider the static model, which offers to the municipality a lottery of contracts,

such that:

1 1

2 2

P 1 P 1 T 1

P 2 P 2 T 1

1(Y , T , Y ,T) ocorra com probabilidade

1 ...

(Y ,T , Y ,T ) ocorra com probabilidade 1 ...

................................................................................

−

−

+ δ + + δ

δ+ δ + + δ

T T

T 1

P T P T T 1

...................

(Y ,T ,Y ,T ) ocorra com probabilidade 1 ...

−

−

δ+ δ + + δ

If a municipality of type θ accepts the contract lottery and reveals its true type, its

expected utility is of:

39

( )

1 1 1 1 1 1

t t t

T 1

M P P 1 P P M P P 1 P PT 1 T 1

Tt 1

M P P t P PT 1t 1

Tt 1

T 1RP dinâmicat 1

1Y N .Y T N . .v(Y ) ... Y N .Y T N . .v(Y )

1 ... 1 ...

1 . Y N .Y T N . .v(Y )1 ...

1 U( )1 ...

U( )

−

− −

−−

=

−−θ

=

δ − + + θ + + − + + θ + δ + + δ + δ + + δ

= δ − + + θ + δ + + δ

≥ δ θ + δ + + δ

= θ

∑

∑

This way, it is verified that the lottery fulfills the participation restriction of a

municipality of type θ in the static model. The verification for type θ is analogous.

In relation to the incentive compatibility restriction for a municipality of type θ , we have

that:

( )

1 1 1 1 1 1

t t t

t

T 1

M P P 1 P P M P P 1 P PT 1 T 1

Tt 1

M P P t P PT 1t 1

Tt 1

M P P t PT 1RCI dinâmicat 1

1 Y N .Y T N . .v(Y ) ... Y N .Y T N . .v(Y )1 ... 1 ...

1. Y N .Y T N . .v(Y )

1 ...

1 . Y N .Y T N .1 ...

−

− −

−−

=

−−θ

=

δ − + + θ + + − + + θ + δ + + δ + δ + + δ

= δ − + + θ + δ + +δ

≥ δ − + + θ+ δ + + δ

∑

∑ ( )tP.v(Y )

For the government, the expected utility from the lottery is:

( ) ( )

( ) ( )

t t t t

t t t t

t 1 t 1T T

F F t P P F t P PT 1 T 1t 1 t 1

T Tt 1 t 1

F t P P F t P PT 1t 1 t 1

F P

U . (Y T ) N .v(Y ) (1 ). (Y T ) N .v(Y )1 ... 1 ...

1. . (Y T ) N .v(Y ) (1 ). . (Y T ) N .v(Y )

1 ...

.((Y T) N

− −

− −= =

− −−

= =

δ δ= π − + + −π − + + δ + +δ + δ + +δ

= π δ − + + − π δ − + + δ + +δ

≤ π − +

∑ ∑

∑ ∑

P F P P

solução ótima do governo no caso estático com informação incompleta

.v(Y )) (1 ).((Y T) N .v(Y ))+ −π − +14444444444244444444443

Therefore,

( ) ( )t t t t

T Tt 1 t 1

F t P P F t P Pt 1 t 1

T Tt 1 t 1

F P P F P Pt 1 t 1

. . (Y T ) N .v(Y ) (1 ). . (Y T ) N .v(Y )

. ((Y T) N .v(Y )) (1 ). ((Y T) N .v(Y ))

− −

= =

− −

= =

π δ − + + − π δ − +

≤ π δ − + + − π δ − +

∑ ∑

∑ ∑

This way, the government’s expected utility in the dynamic case cannot be greater than in

the static case, being the same if the government repeats the static solution for each T periods of

the contract’s lifetime.

International Poverty CentreSBS – Ed. BNDES, 10º andar70076-900 Brasilia DFBrazil

povertycentre@undp-povertycentre.orgwww.undp.org/povertycentreTelephone +55 61 2105 5000